2 Answers
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It let's you define how much a certain operation in the EVM (Ethereum Virtual Machine) should cost in relation to each other. In this sense it is a cost structure.

The benefit is to decouple the incentive structure for cheap opcodes from a certain price. If the value of ETH increases, miners can choose to lower their demand for fees in ether smoothly. So with this, a mining fee market can always adapt to ETH valuation.

The user that sends a transaction to a contract can pick any gas price, but the miners don't have to accepted it. It is a market.
– Roland KoflerJun 3 '16 at 8:28

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You mean the miners pay the price and the sender benefits from it? Or it is exactly the other way? excuse me if this is a dumb Q
– varDumperJun 3 '16 at 8:31

No the sender proposes a gasPrice he has to pay. The miner can accept it or refuse it because it is too low. There is a default gas price of 10 Szabo currently. 1 ETH is 1 million Szabo.
– Roland KoflerJun 3 '16 at 8:37

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Ok, so at the end it's the miner who benefits from the gasPrice right?
– varDumperJun 3 '16 at 8:39

Ethereum is essentially a single Quasi Turing-complete computer, capable of computation just like any other computer, except for every instruction executed, there must be something expendable known as gas. Gas is essentially a limited resource required to run computation to ensure that every contract will halt/terminate and did not cause Denial of Service.